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#1 2024-05-07 11:02:54

mathxyz
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From: Brooklyn, NY
Registered: 2024-02-24
Posts: 1,053

Rational Number Raised To Rational Power

Give an example in which the result of raising a rational number to a rational power is an irrational number.

You say?

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#2 2024-05-07 19:26:37

Bob
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Registered: 2010-06-20
Posts: 10,627

Re: Rational Number Raised To Rational Power

Raising to power 1/2 can result in an irrational.

B


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2024-05-08 02:10:14

mathxyz
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From: Brooklyn, NY
Registered: 2024-02-24
Posts: 1,053

Re: Rational Number Raised To Rational Power

Bob wrote:

Raising to power 1/2 can result in an irrational.

B

Wow! This is easier than the problem makes it seems. I will return later with my work.

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#4 2024-05-08 10:21:55

mathxyz
Member
From: Brooklyn, NY
Registered: 2024-02-24
Posts: 1,053

Re: Rational Number Raised To Rational Power

nycguitarguy wrote:
Bob wrote:

Raising to power 1/2 can result in an irrational.

B

Wow! This is easier than the problem makes it seems. I will return later with my work.

3 Samples

How about 2^(1/3)?

How about 5^(1/7)?

How about 100^(1/100)?

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#5 2024-05-09 05:37:33

Bob
Administrator
Registered: 2010-06-20
Posts: 10,627

Re: Rational Number Raised To Rational Power

All good.

B


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#6 2024-05-09 07:47:24

mathxyz
Member
From: Brooklyn, NY
Registered: 2024-02-24
Posts: 1,053

Re: Rational Number Raised To Rational Power

Bob wrote:

All good.

B

Very good.

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